JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 5)
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to
7
6
5
4
Explanation
$$\begin{aligned}
& a+a r+a r^2+a r^3+\ldots .+a r^{63} \\
& =7\left(a+a r^2+a r^4 \ldots .+a r^{62}\right) \\
& \Rightarrow \frac{a\left(1-r^{64}\right)}{1-r}=\frac{7 a\left(1-r^{64}\right)}{1-r^2} \\
& r=6
\end{aligned}$$
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